Datasheet

f
O
=
10
-
(V + 1)
C
2 RCp
Frequency (Hz)
1 10 100 1k 10k 100k 1M 10M 100M
G = +40dB
G = +15dB
G = 15dB-
G = 40dB-
A
OL
100
90
80
70
60
50
40
30
20
10
0
Gain (dB)
=
s +
2
+
G
R C
2 2
s
nRC
s
nRC
-
V
V
O
I
Q = n ·
10
-
(V + 1)
C
VCA810
www.ti.com SBOS275F –JUNE 2003–REVISED DECEMBER 2010
Another factor limits the high-frequency performance VOLTAGE-CONTROLLED BAND-PASS
of the resulting high-pass filter: the finite bandwidth of FILTER
the op amp. This limits the frequency duration of the
The variable gain of the VCA810 also provides
equalizer response. Limitations such as bandwidth
voltage control over the center frequency of a
and stability are clearly shown in Figure 42.
band-pass filter. As shown in Figure 43, this filter
follows from the state-variable configuration with the
VCA810 replacing the inverter common to that
configuration. Variation of the VCA810 gain moves
the filter’s center frequency through a 100:1 range
following the relationship of Equation 5:
(5)
As before, variable gain controls a circuit time
constant to vary the filter response. The gain of the
VCA810 amplifies or attenuates the signal driving the
lower integrator of the circuit. This amplification alters
the effective resistance of the integrator time
constant, producing the response of Equation 6:
Figure 42. Amplifier Noise Gain and A
OL
for
Different Gain
(6)
Evaluation of this response equation reveals a
Other limitations of this circuit are stability versus
passband gain of A
O
= –1, a bandwidth of BW =
VCA810 gain and input signal level for the circuit.
Figure 42 also illustrates these two factors. As the
1/(2pRC), and a selectivity of . Note
VCA810 gain increases, the crossover slope between
that variation of control voltage V
C
alters Q but not
the A
OL
curve of the OPA846 and noise gain will be
bandwidth.
greater than 20dB/decade, rendering the circuit
The gain provided by the VCA810 restricts the output
unstable. The signal level for high gain of the
swing of the filter. Output signal V
O
must be
VCA810 will meet two limitations: the output voltage
constrained to a level that does not drive the VCA810
swings of both the VCA810 and the OPA846. The
output, V
OA
, into its saturation limit. Note that these
expression V
OA
= GV
I
relates these two voltages.
two outputs have voltage swings related by V
OA
=
Thus, an output voltage limit V
OAL
constrains the input
G
VO
. Thus, a swing limit V
OAL
imposes a circuit output
voltage to V
I
≤ V
OAL
/G.
limit of V
OL
≤ V
OAL
/G.
With the components shown, BW = 50kHz. This
See Figure 44 for the frequency response for two
bandwidth provides an integrator response duration
different gain conditions of the schematic shown in
of four decades of frequency for f
Z
= 1Hz, dropping to
Figure 43. In particular, notice the center frequency
one decade for f
Z
= 10kHz.
shift and the selectivity of Q changing as the gain is
increased.
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